Laws of refraction

The idea

The incident ray, the refracted ray and the normal at the point of incidence lie in one plane, and for light of a given colour and pair of media sin i / sin r is constant (Snell's law).

A steady number

Scientists measured the angle of incidence i and the angle of refraction r for many rays going from air into water. They found a pattern.

As the angle of incidence is changed, what do you think stays the same?

• The ratio of sin i to sin r
• The angle of refraction
• The difference i − r

Same ratio every time

Set i to 20°, 40° and 60° for water. Then switch to glass. Watch the last readout.

Snell's law

For water the ratio stayed 1.33 for every angle. For glass it was a different constant, 1.52. A new angle gave new sin i and sin r, but the ratio stayed.

The laws of refraction: (i) the incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane. (ii) For light of a given colour and a given pair of media, sin i ÷ sin r is a constant. This is Snell's law.

Notes

The incident ray, refracted ray and normal lie in one plane, and sin i ÷ sin r is constant for light of a given colour and a given pair of media (Snell's law).

Check yourself

According to the first law of refraction, the incident ray, the refracted ray and the normal

What does Snell's law say about sin i ÷ sin r for a given pair of media and a given colour of light?

For light going from air into glass, sin i ÷ sin r = 1.52. If sin i = 0.76, what is sin r?

Answer: 0.5

sin r = sin i ÷ 1.52 = 0.76 ÷ 1.52 = 0.5.

Light of one colour goes from air into water at 30° and again at 50°. What is the same both times?

• are all at right angles to each other. The normal is at right angles to the surface, but the two rays are not at right angles to each other. All three lie in one plane.
• lie in three different planes. The first law says they all lie in the same plane.
• all lie in the same plane — correct. Yes!
• It is a constant — correct. Yes!
• It changes with the angle of incidence. The ratio stays the same for every angle of incidence, as the readouts showed.
• It is always equal to i ÷ r. The law is about the sines of the angles. The ratio of the angles themselves is not constant.
• The angle of refraction. A different angle of incidence gives a different angle of refraction.
• The value of sin i ÷ sin r — correct. Yes!
• The difference between i and r. The difference changes when the angles change. Only the ratio of the sines stays the same.